diff --git a/src/emsarray/conventions/_base.py b/src/emsarray/conventions/_base.py
index e35c38f1..22ef190c 100644
--- a/src/emsarray/conventions/_base.py
+++ b/src/emsarray/conventions/_base.py
@@ -30,9 +30,9 @@
 if TYPE_CHECKING:
     # Import these optional dependencies only during type checking
     from cartopy.crs import CRS
+    from cartopy.mpl.geoaxes import GeoAxes
     from matplotlib.animation import FuncAnimation
-    from matplotlib.axes import Axes
-    from matplotlib.collections import PolyCollection
+    from matplotlib.collections import Collection, PolyCollection
     from matplotlib.figure import Figure
     from matplotlib.quiver import Quiver
 
@@ -935,6 +935,7 @@ def data_crs(self) -> 'CRS':
     def plot_on_figure(
         self,
         figure: 'Figure',
+        *variables: DataArrayOrName | tuple[DataArrayOrName, ...],
         scalar: DataArrayOrName | None = None,
         vector: tuple[DataArrayOrName, DataArrayOrName] | None = None,
         title: str | None = None,
@@ -971,26 +972,30 @@ def plot_on_figure(
         :func:`.plot.plot_on_figure` : The underlying implementation
         """
         if scalar is not None:
-            kwargs['scalar'] = utils.name_to_data_array(self.dataset, scalar)
+            variables = variables + (scalar,)
 
         if vector is not None:
-            kwargs['vector'] = tuple(utils.name_to_data_array(self.dataset, v) for v in vector)
+            variables = variables + (vector,)
+
+        mapped_variables: list[xarray.DataArray | tuple[xarray.DataArray, ...]] = []
+        for variable in variables:
+            if isinstance(variable, tuple):
+                mapped_variables.append(tuple(
+                    utils.name_to_data_array(self.dataset, v)
+                    for v in variable
+                ))
+            else:
+                mapped_variables.append(utils.name_to_data_array(self.dataset, variable))
 
         if title is not None:
             kwargs['title'] = title
-        elif scalar is not None and vector is None:
-            # Make a title out of the scalar variable, but only if a title
-            # hasn't been supplied and we don't also have vectors to plot.
-            #
-            # We can't make a good name from vectors,
-            # as they are in two variables with names like
-            # 'u component of current' and 'v component of current'.
-            #
-            # Users can supply their own titles
-            # if this automatic behaviour is insufficient
-            kwargs['title'] = make_plot_title(self.dataset, kwargs['scalar'])
 
-        plot_on_figure(figure, self, **kwargs)
+        # Find a title if there is a single variable passed in
+        elif len(variables) == 1 and isinstance(variables[0], xarray.DataArray):
+            variable = variables[0]
+            kwargs['title'] = make_plot_title(self.dataset, variable)
+
+        plot_on_figure(figure, self, *mapped_variables, **kwargs)
 
     @_requires_plot
     def plot(self, *args: Any, **kwargs: Any) -> None:
@@ -1111,6 +1116,73 @@ def animate_on_figure(
 
         return animate_on_figure(figure, self, coordinate=coordinate, **kwargs)
 
+    @_requires_plot
+    def plot_on_axes(
+        self,
+        axes: 'GeoAxes',
+        variable: xarray.DataArray | tuple[xarray.DataArray, ...],
+        **kwargs: Any,
+    ) -> 'Collection':
+        if isinstance(variable, xarray.DataArray):
+            grid_kind = self.get_grid_kind(variable)
+            if grid_kind is self.default_grid_kind:
+                return self.plot_polygons_on_axes(axes, variable)
+
+            raise ValueError(f"Not able to plot variable {variable.name!r}, grid kind {grid_kind}")
+
+        else:
+            names = tuple(v.name for v in variable)
+            grid_kinds = tuple(self.get_grid_kind(v) for v in variable)
+            if len(variable) == 2 and grid_kinds == (self.default_grid_kind, self.default_grid_kind):
+                return self.plot_vector_components_on_axes(axes, variable)
+
+            raise ValueError(f"Not able to plot variables {names!r}, grid kinds {grid_kinds!r}")
+
+    @_requires_plot
+    def plot_polygons_on_axes(
+        self,
+        axes: 'GeoAxes',
+        data_array: xarray.DataArray | None,
+        colorbar: bool = True,
+        **kwargs: Any,
+    ) -> 'Collection':
+        defaults = dict(cmap='jet', edgecolor='face')
+        kwargs = {**defaults, **kwargs}
+
+        collection = self.make_poly_collection(data_array, **kwargs)
+        axes.add_collection(collection)
+
+        if colorbar and data_array is not None:
+            units = data_array.attrs.get('units')
+            axes.get_figure().colorbar(collection, ax=axes, location='right', label=units)
+
+        return collection
+
+    @_requires_plot
+    def plot_vector_components_on_axes(
+        self,
+        axes: 'GeoAxes',
+        components: tuple[xarray.DataArray, xarray.DataArray],
+        **kwargs: Any,
+    ) -> 'Collection':
+        u, v = components
+        quiver = self.make_quiver(axes, u, v, **kwargs)
+        axes.add_collection(quiver)
+        return quiver
+
+    @_requires_plot
+    def plot_geometry_on_axes(
+        self,
+        axes: 'GeoAxes',
+        **kwargs: Any,
+    ) -> 'Collection':
+        """
+        Plot the geometry of this dataset on to some Axes
+        """
+        collection = self.make_poly_collection()
+        axes.add_collection(collection)
+        return collection
+
     @_requires_plot
     @utils.timed_func
     def make_poly_collection(
@@ -1120,7 +1192,7 @@ def make_poly_collection(
     ) -> 'PolyCollection':
         """
         Make a :class:`~matplotlib.collections.PolyCollection`
-        from the geometry of this :class:`~xarray.Dataset`.
+        from the polygon geometry of this :class:`~xarray.Dataset`.
         This can be used to make custom matplotlib plots from your data.
 
         If a :class:`~xarray.DataArray` is passed in,
@@ -1190,32 +1262,23 @@ def make_poly_collection(
 
         return polygons_to_collection(self.polygons[self.mask], **kwargs)
 
-    def make_patch_collection(
-        self,
-        data_array: DataArrayOrName | None = None,
-        **kwargs: Any,
-    ) -> 'PolyCollection':
-        warnings.warn(
-            "Convention.make_patch_collection has been renamed to "
-            "Convention.make_poly_collection, and now returns a PolyCollection",
-            category=DeprecationWarning,
-        )
-        return self.make_poly_collection(data_array, **kwargs)
-
     @_requires_plot
     def make_quiver(
         self,
-        axes: 'Axes',
+        axes: 'GeoAxes',
         u: DataArrayOrName | None = None,
         v: DataArrayOrName | None = None,
         **kwargs: Any,
     ) -> 'Quiver':
         """
         Make a :class:`matplotlib.quiver.Quiver` instance to plot vector data.
+        The vectors will be placed at the centre of each polygon of the dataset.
+        The data arrays `u` and `v` represent the `x` and `y` vector components
+        for each polygon.
 
         Parameters
         ----------
-        axes : matplotlib.axes.Axes
+        axes : matplotlib.axes.GeoAxes
             The axes to make this quiver on.
         u, v : xarray.DataArray or str, optional
             The DataArrays or the names of DataArrays in this dataset
diff --git a/src/emsarray/conventions/ugrid.py b/src/emsarray/conventions/ugrid.py
index e3675a09..0306b00b 100644
--- a/src/emsarray/conventions/ugrid.py
+++ b/src/emsarray/conventions/ugrid.py
@@ -14,7 +14,7 @@
 from contextlib import suppress
 from dataclasses import dataclass
 from functools import cached_property
-from typing import Any, cast
+from typing import TYPE_CHECKING, Any, cast
 
 import numpy
 import shapely
@@ -25,10 +25,16 @@
 from emsarray.exceptions import (
     ConventionViolationError, ConventionViolationWarning
 )
+from emsarray.operations import triangulate
+from emsarray.plot import _requires_plot
 from emsarray.types import Bounds, Pathish
 
 from ._base import DimensionConvention, Specificity
 
+if TYPE_CHECKING:
+    from matplotlib.axes import Axes
+    from matplotlib.collections import Collection
+
 logger = logging.getLogger(__name__)
 
 
@@ -1345,3 +1351,50 @@ def drop_geometry(self) -> xarray.Dataset:
         dataset = super().drop_geometry()
         dataset.attrs.pop('Conventions', None)
         return dataset
+
+    @_requires_plot
+    def plot_on_axes(
+        self,
+        axes: 'Axes',
+        variable: xarray.DataArray | tuple[xarray.DataArray, ...],
+        **kwargs: Any,
+    ) -> 'Collection':
+        if isinstance(variable, xarray.DataArray):
+            grid_kind = self.get_grid_kind(variable)
+            if grid_kind is UGridKind.node:
+                return self.plot_tripcolor_on_axes(axes, variable, **kwargs)
+
+        return super().plot_on_axes(axes, variable, **kwargs)
+
+    def plot_tripcolor_on_axes(
+        self,
+        axes: 'Axes',
+        data_array: xarray.DataArray,
+        *,
+        shading: str = 'gouraud',
+        **kwargs: Any,
+    ) -> 'Collection':
+        collection = self.make_tripcolor(axes, data_array, **kwargs)
+        axes.add_collection(collection)
+        return collection
+
+    def make_tripcolor(
+        self,
+        axes: 'Axes',
+        data_array: xarray.DataArray | None = None,
+        *,
+        shading: str = 'gouraud',
+        **kwargs: Any,
+    ) -> 'Collection':
+        import matplotlib.tri
+
+        topology = self.topology
+        vertices = numpy.c_[topology.node_x.values, topology.node_y.values].T
+
+        _vertices, triangles, _face_indices = triangulate.triangulate_dataset(self.dataset, vertices=vertices)
+        triangulation = matplotlib.tri.Triangulation(vertices[:, 0], vertices[:, 1], triangles)
+
+        data_array = utils.name_to_data_array(self.dataset, data_array)
+
+        collection = axes.tripcolor(triangulation, data_array.values, shading='gouraud', **kwargs)
+        return collection
diff --git a/src/emsarray/operations/triangulate.py b/src/emsarray/operations/triangulate.py
index b0a2bcc4..aa47b318 100644
--- a/src/emsarray/operations/triangulate.py
+++ b/src/emsarray/operations/triangulate.py
@@ -1,6 +1,8 @@
 """
 Operations for making a triangular mesh out of the polygons of a dataset.
 """
+from typing import Any
+
 import numpy
 import pandas
 import shapely
@@ -14,6 +16,8 @@
 
 def triangulate_dataset(
     dataset: xarray.Dataset,
+    *,
+    vertices: numpy.ndarray[tuple[Any, ...], numpy.dtype[Any]] | None = None,
 ) -> tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]:
     """
     Triangulate the polygon cells of a dataset
@@ -93,11 +97,14 @@ def triangulate_dataset(
     """
     polygons = dataset.ems.polygons
 
-    # Find all the unique coordinates and assign them each a unique index
-    all_coords = shapely.get_coordinates(polygons)
-    vertex_index = pandas.MultiIndex.from_arrays(all_coords.T).drop_duplicates()
+    if vertices is None:
+        # Find all the unique coordinates and assign them each a unique index
+        all_coords = shapely.get_coordinates(polygons)
+        vertex_index = pandas.MultiIndex.from_arrays(all_coords.T).drop_duplicates()
+        vertices = numpy.array(vertex_index.to_list())
+    else:
+        vertex_index = pandas.MultiIndex.from_arrays(list(vertices))
     vertex_series = pandas.Series(numpy.arange(len(vertex_index)), index=vertex_index)
-    vertex_coords = numpy.array(vertex_index.to_list())
 
     polygon_length = shapely.get_num_coordinates(polygons)
 
@@ -191,7 +198,7 @@ def _add_triangles(face_index: int, vertex_triangles: numpy.ndarray) -> None:
     faces = joined_df['face_indices'].to_numpy()
     triangles = joined_df[['v0', 'v1', 'v2']].to_numpy()
 
-    return vertex_coords, triangles, faces
+    return vertices, triangles, faces
 
 
 def _triangulate_polygons_by_length(polygons: numpy.ndarray) -> numpy.ndarray:
diff --git a/src/emsarray/plot.py b/src/emsarray/plot.py
index 7acf2864..708738c8 100644
--- a/src/emsarray/plot.py
+++ b/src/emsarray/plot.py
@@ -274,7 +274,8 @@ def make_plot_title(
 def plot_on_figure(
     figure: Figure,
     convention: 'conventions.Convention',
-    *,
+    *variables: xarray.DataArray | tuple[xarray.DataArray, ...],
+    axes: GeoAxes | None = None,
     scalar: xarray.DataArray | None = None,
     vector: tuple[xarray.DataArray, xarray.DataArray] | None = None,
     title: str | None = None,
@@ -315,31 +316,30 @@ def plot_on_figure(
     coast : bool, default True
         Whether to add coastlines to the plot using :func:`add_coast()`.
     """
-    if projection is None:
-        projection = cartopy.crs.PlateCarree()
-
-    axes: GeoAxes = figure.add_subplot(projection=projection)
-    axes.set_aspect(aspect='equal', adjustable='datalim')
-
-    if scalar is None and vector is None:
-        # Plot the polygon shapes for want of anything else to draw
-        collection = convention.make_poly_collection()
-        axes.add_collection(collection)
-        if title is None:
-            title = 'Geometry'
 
+    # Support old syntax of separately specifying scalar and vector items to plot.
+    # This will be deprecated soon.
     if scalar is not None:
-        # Plot a scalar variable on the polygons using a colour map
-        collection = convention.make_poly_collection(
-            scalar, cmap='jet', edgecolor='face')
-        axes.add_collection(collection)
-        units = scalar.attrs.get('units')
-        figure.colorbar(collection, ax=axes, location='right', label=units)
-
+        variables = variables + (scalar,)
     if vector is not None:
-        # Plot a vector variable using a quiver
-        quiver = convention.make_quiver(axes, *vector)
-        axes.add_collection(quiver)
+        variables = variables + (vector,)
+
+    # Construct some axes if we don't have any
+    if axes is None:
+        if projection is None:
+            projection = cartopy.crs.PlateCarree()
+        axes = figure.add_subplot(projection=projection)
+        axes.set_aspect(aspect='equal', adjustable='datalim')
+
+    # Plot everything we have
+    for var in variables:
+        convention.plot_on_axes(axes, var)
+
+    # Plot the geometry of the dataset if there are no variables passed in
+    if len(variables) == 0:
+        convention.plot_geometry_on_axes(axes)
+        if title is None:
+            title = 'Geometry'
 
     if title:
         axes.set_title(title)
@@ -349,17 +349,12 @@ def plot_on_figure(
 
     if coast:
         add_coast(axes)
+
     if gridlines:
         add_gridlines(axes)
 
     axes.autoscale()
 
-    # Work around for gridline positioning issues
-    # https://github.com/SciTools/cartopy/issues/2245#issuecomment-1732313921
-    layout_engine = figure.get_layout_engine()
-    if layout_engine is not None:
-        layout_engine.execute(figure)
-
 
 @_requires_plot
 def animate_on_figure(